¶ 1994 AMC8 Problems and Solutions
Problem Set Workbook
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Discussion Forum
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Individual Problems and Solutions
For problems and detailed solutions to each of the 1994 AMC8 problems, please refer below:
Problem 1: Which of the following is the largest?
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Problem 2:
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Problem 3: Each day Maria must work hours. This does not include the minutes she takes for lunch. If she begins working at A.M. and takes her lunch break at noon, then her working day will end at
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Problem 4: Which of the following represents the result when the figure shown at the right is rotated clockwise about its center?
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Problem 5: Given that mile furlongs and furlong rods, the number of rods in one mile is
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Problem 6: The unit's digit (one's digit) of the product of any six consecutive positive whole numbers is
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Problem 7: If and , then
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Problem 8: For how many three-digit whole numbers does the sum of the digits equal
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Problem 9: A shopper buys a coat on sale for off. An additional is taken off the sale price by using a discount coupon. A sales tax of is paid on the final selling price. The total amount the shopper pays for the coat is
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Problem 10: For how many positive integer values of is the expression an integer?
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Problem 11: Last summer students attended basketball camp. Of those attending, were boys and were girls. Also, students were from Jones Middle School and were from Clay Middle School. Twenty oí the girls were from Jones Middle School. How many of the boys were from Clay Middle School?
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Problem 12: Each of the three large squares shown below is the same size. Segments that intersect the sides of the squares intersect at the midpoints of the sides. How do the shaded areas of these squares compare?
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A. The shaded areas in all three are equal.
B. Only the shaded areas of and are equal.
C. Only the shaded areas of and are equal.
D. Only the shaded areas of and are equal.
E. The shaded areas of and are all different.
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Problem 13: The number halfway between and is
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Problem 14: Two children at a time can play pairball. For minutes, with only two children playing at one time, five children take turns so that each one plays the same amount of time. The number of minutes each child plays is
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Problem 15: If this path is to continue in the same pattern then which sequence of arrows goes from point to point
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Problem 16: The perimeter of one square is times the perimeter of another square. The area of the larger square is how many times the area of the smaller square?
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Problem 17: Pauline Bunyan can shovel snow at the rate of cubic yards for the first hour, cubic yards for the second, for the third, etc., always shoveling one cubic yard less per hour than the previous hour. If her driveway is yards wide, yards long, and covered with snow yards deep, then the number of hours it will take her to shovel it clean is closest to
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Problem 18: Mike leaves home and drives slowly east through city traffic. When he reaches the highway he drives east more rapidly until he reaches the shopping mall where he stops. He shops at the mall for an hour. Mike returns home by the same route as he came, driving west rapidly along the highway and then slowly through city traffic. Each graph shows the distance from home on the vertical axis versus the time elapsed since leaving home on the horizontal axis. Which graph is the best representation of Mike's trip?
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Problem 19: Around the outside of a by square, construct four semicircles (as shown in the figure) with the four sides of the square as their diameters. Another square, , has its sides parallel to the corresponding sides of the original square, and each side of is tangent to one of the semicircles. The area of the square is
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Problem 20: Let and be four different digits selected from the set
If the sum is to be as small as possible, then must equal
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Problem 21: A gumball machine contains red, white, and blue gumballs. The least number of gumballs a person must buy to be sure of getting four gumballs of the same color is
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Problem 22: The two wheels shown at the right are spun and the two resulting numbers are added. The probability that the sum of the two numbers is even is
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Problem 23: If and are different digits, then the largest possible -digit sum for
has the form
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Problem 24: A by square is divided into four by squares. Each of the small squares is to be painted either green or red. In how many different ways can the painting be accomplished so that no green square shares its top or right side with any red square? There may be as few as zero or as many as four small green squares.
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Problem 25: Find the sum of the digits in the answer to
where a string of nines is multiplied by a string of fours.
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The problems on this page are the property of the MAA's American Mathematics Competitions